From past records of highway construction and maintenance costs, a state highway departmen...

From past records of highway construction and maintenance costs, a state highway department determines the following cost relationships for two-lane bituminous highways within the state:

cc(x) = 0.1x20

cm(x) =

where the equation hold for (0.5 ≤ x ≤ 10.0) and where

x = payment thickness (inches);

cc(x) = annualized construction cost (millions of dollars per mile per year); and

cm(x) = annual maintenance cost (millions of dollars per mile per year).

(a) In words, describe the basic tradeoff decision that the highway department must make.

(b) Determine the optimal pavement thickness, justifying the type of point found.

(c) If pavement thickness can be specified only in whole inches, what is the best pavement thickness caused by field construction condition? How sensitive is the optimal cost to small changes in thickness?